We can generalize the above definition to the case of a mapping . Now, we define a limit point of to be an such that for all there exist infinitely many such that
We then define , to be the supremum of all the limit points of , or if there are no limit points. We recover the previous definition as a special case by considering the limit superior of the inclusion mapping .
Since a sequence of real numbers is just a mapping from to , we may adapt the above definition to arrive at the notion of the limit superior of a sequence. However for the case of sequences, an alternative, but equivalent definition is available. For each , let be the supremum of the tail,
This construction produces a non-increasing sequence
|Date of creation||2013-03-22 12:21:58|
|Last modified on||2013-03-22 12:21:58|
|Last modified by||rmilson (146)|